Extreme Data Mining: Inference from Small Datasets

Neural networks have been applied successfully in many fields. However, satisfactory results can only be found under large sample conditions. When it comes to small training sets, the performance may not be so good, or the learning task can even not be accomplished. This deficiency limits the applications of neural network severely. The main reason why small datasets cannot provide enough information is that there exist gaps between samples, even the domain of samples cannot be ensured. Several computational intelligence techniques have been proposed to overcome the limits of learning from small datasets. We have the following goals: i. To discuss the meaning of small in the context of inferring from small datasets. ii. To overview computational intelligence solutions for this problem. iii. To illustrate the introduced concepts with a real-life application

Complexity of certificates, heuristics, and counting types , with applications to cryptography and circuit theory

In dieser Habilitationsschrift werden Struktur und Eigenschaften von Komplexitätsklassen wie P und NP untersucht, vor allem im Hinblick auf: Zertifikatkomplexität, Einwegfunktionen, Heuristiken gegen NP-Vollständigkeit und Zählkomplexität. Zum letzten Punkt werden speziell untersucht: (a) die Komplexität von Zähleigenschaften von Schaltkreisen, (b) Separationen von Zählklassen mit Immunität und (c) die Komplexität des Zählens der Lösungen von ,,tally`` NP-Problemen

Relativizations of the P-Printable Sets and the Sets with Small Generalized Kolmogorov Complexity

Although tally sets are generally considered to be weak when used as oracles, it is shown here that in relativizing certain complexity classes, they are in fact no less powerful than any other class of sets and are more powerful than the class of recursive sets. More specifically, relativizations of the classes of P-printable sets and sets with small Generalized Kolmogorov complexity (SGK) are studied. It is shown here that all sparse sets are P TALLY -printable and are in SGK TALLY , and that there are self-P-printable sets that are neither P REC -printable nor in SGK REC . There are also sets that are P REC -printable and in SGK REC that are not self-P-printable. Relativizations to various subrecursive oracles are also presented. A restriction on the number of oracle queries is also presented, with the result that relativizing SGK to any oracle with at most O(log n) queries results in a set that is still in SGK. 1 Introduction Tally sets have generally been considered wea..